Arithmetical functions :: an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties /
The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mea...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
©1994.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
184. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related multiplicative functions. They also prove the mean-value theorems of Wirsing and Halász and study the pointwise convergence of the Ramanujan expansion. Finally, some applications to power series with multiplicative coefficients are included, along with exercises and an extensive bibliography. |
| Beschreibung: | 1 online resource (xix, 367 pages) : illustrations, portraits |
| Bibliographie: | Includes bibliographical references (pages 333-352) and indexes. |
| ISBN: | 9781107359963 1107359961 9781461938262 1461938260 1299820751 9781299820753 1139884808 9781139884808 1107383749 9781107383746 1107299136 9781107299139 1107390184 9781107390188 1107387337 9781107387331 1107398606 9781107398603 |
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| 520 | |a The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related multiplicative functions. They also prove the mean-value theorems of Wirsing and Halász and study the pointwise convergence of the Ramanujan expansion. Finally, some applications to power series with multiplicative coefficients are included, along with exercises and an extensive bibliography. | ||
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| id | ZDB-4-EBA-ocn847520384 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:25:23Z |
| institution | BVB |
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| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge University Press, |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Schwarz, Wolfgang, 1934-2013. https://id.oclc.org/worldcat/entity/E39PBJfrHwwwpMBYKpYkqWfDv3 Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / Wolfgang Schwarz, Jürgen Spilker. Cambridge ; New York : Cambridge University Press, ©1994. 1 online resource (xix, 367 pages) : illustrations, portraits text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 184 Includes bibliographical references (pages 333-352) and indexes. Print version record. English. The aim of this book is to characterize certain multiplicative and additive arithmetical functions by combining methods from number theory with some simple ideas from functional and harmonic analysis. The authors achieve this goal by considering convolutions of arithmetical functions, elementary mean-value theorems, and properties of related multiplicative functions. They also prove the mean-value theorems of Wirsing and Halász and study the pointwise convergence of the Ramanujan expansion. Finally, some applications to power series with multiplicative coefficients are included, along with exercises and an extensive bibliography. Arithmetic functions. http://id.loc.gov/authorities/subjects/sh85007174 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Mean value theorems (Calculus) http://id.loc.gov/authorities/subjects/sh85082689 Fonctions arithmétiques. Théorie des nombres. Théorème des accroissements finis. MATHEMATICS Algebra Intermediate. bisacsh Arithmetic functions fast Mean value theorems (Calculus) fast Number theory fast Zahlentheoretische Funktion gnd Speciale functies (wiskunde) gtt Teoria analítica dos números. larpcal Fonctions arithmétiques. ram Nombres, théorie des. ram Number theory Spilker, Jürgen. http://id.loc.gov/authorities/names/nr94020367 Print version: Schwarz, Wolfgang, 1934- Arithmetical functions. Cambridge ; New York : Cambridge University Press, ©1994 0521427258 (DLC) 94195490 (OCoLC)30367457 London Mathematical Society lecture note series ; 184. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616947 Volltext |
| spellingShingle | Schwarz, Wolfgang, 1934-2013 Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / London Mathematical Society lecture note series ; Arithmetic functions. http://id.loc.gov/authorities/subjects/sh85007174 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Mean value theorems (Calculus) http://id.loc.gov/authorities/subjects/sh85082689 Fonctions arithmétiques. Théorie des nombres. Théorème des accroissements finis. MATHEMATICS Algebra Intermediate. bisacsh Arithmetic functions fast Mean value theorems (Calculus) fast Number theory fast Zahlentheoretische Funktion gnd Speciale functies (wiskunde) gtt Teoria analítica dos números. larpcal Fonctions arithmétiques. ram Nombres, théorie des. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85007174 http://id.loc.gov/authorities/subjects/sh85093222 http://id.loc.gov/authorities/subjects/sh85082689 |
| title | Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / |
| title_auth | Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / |
| title_exact_search | Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / |
| title_full | Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / Wolfgang Schwarz, Jürgen Spilker. |
| title_fullStr | Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / Wolfgang Schwarz, Jürgen Spilker. |
| title_full_unstemmed | Arithmetical functions : an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / Wolfgang Schwarz, Jürgen Spilker. |
| title_short | Arithmetical functions : |
| title_sort | arithmetical functions an introduction to elementary and analytic properties of arithmetic functions and to some of their almost periodic properties |
| title_sub | an introduction to elementary and analytic properties of arithmetic functions and to some of their almost-periodic properties / |
| topic | Arithmetic functions. http://id.loc.gov/authorities/subjects/sh85007174 Number theory. http://id.loc.gov/authorities/subjects/sh85093222 Mean value theorems (Calculus) http://id.loc.gov/authorities/subjects/sh85082689 Fonctions arithmétiques. Théorie des nombres. Théorème des accroissements finis. MATHEMATICS Algebra Intermediate. bisacsh Arithmetic functions fast Mean value theorems (Calculus) fast Number theory fast Zahlentheoretische Funktion gnd Speciale functies (wiskunde) gtt Teoria analítica dos números. larpcal Fonctions arithmétiques. ram Nombres, théorie des. ram |
| topic_facet | Arithmetic functions. Number theory. Mean value theorems (Calculus) Fonctions arithmétiques. Théorie des nombres. Théorème des accroissements finis. MATHEMATICS Algebra Intermediate. Arithmetic functions Number theory Zahlentheoretische Funktion Speciale functies (wiskunde) Teoria analítica dos números. Nombres, théorie des. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=616947 |
| work_keys_str_mv | AT schwarzwolfgang arithmeticalfunctionsanintroductiontoelementaryandanalyticpropertiesofarithmeticfunctionsandtosomeoftheiralmostperiodicproperties AT spilkerjurgen arithmeticalfunctionsanintroductiontoelementaryandanalyticpropertiesofarithmeticfunctionsandtosomeoftheiralmostperiodicproperties |